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In the top ten finishers of a cycling race, 4 were Italians and 8 represented the Telefonica team. How many cyclists from the Telefonica team in the top ten were not Italian?
(1) 2 of the top ten finishers who were Italian did not represent the Telefonica team.
(2) Every cyclist who finished in the top ten was either Italian, represented Telefonica team, or both.
M14-19
(1) 2 of the top ten finishers who were Italian did not represent the Telefonica team.
(2) Every cyclist who finished in the top ten was either Italian, represented Telefonica team, or both.
M14-19
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13 Oct 2013, 09:13
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Official Solution:
In the top ten finishers of a cycling race, 4 were Italians and 8 represented the Telefonica team. How many cyclists from the Telefonica team in the top ten were not Italian?
(1) 2 of the top ten finishers who were Italian did not represent the Telefonica team.
Since 2 out of the 4 Italians in the top 10 did not represent the Telefonica team, it follows that the remaining 2 Italians must have been part of the Telefonica team. Thus, out of the 8 cyclists who represented the Telefonica team, 8 - 2 = 6 were not Italians. Therefore, statement (1) is sufficient.
(2) Every cyclist who finished in the top ten was either Italian, represented Telefonica team, or both.
The given statement implies that there were no cyclists in the top 10 who were neither Italian nor representing the Telefonica team. Using the formula \(\{Total\} = \{Italians\} + \{Telefonica\} - \{Both\}\), we can find that \(\{Both\} = 2\). Since 2 of the top finishers were both Italian and representing Telefonica teams, there were 8 - 2 = 6 top finishers who represented Telefonica but were not Italian. Thus, statement (2) is also sufficient to answer the question.
Answer: D.
In the top ten finishers of a cycling race, 4 were Italians and 8 represented the Telefonica team. How many cyclists from the Telefonica team in the top ten were not Italian?
(1) 2 of the top ten finishers who were Italian did not represent the Telefonica team.
Since 2 out of the 4 Italians in the top 10 did not represent the Telefonica team, it follows that the remaining 2 Italians must have been part of the Telefonica team. Thus, out of the 8 cyclists who represented the Telefonica team, 8 - 2 = 6 were not Italians. Therefore, statement (1) is sufficient.
(2) Every cyclist who finished in the top ten was either Italian, represented Telefonica team, or both.
The given statement implies that there were no cyclists in the top 10 who were neither Italian nor representing the Telefonica team. Using the formula \(\{Total\} = \{Italians\} + \{Telefonica\} - \{Both\}\), we can find that \(\{Both\} = 2\). Since 2 of the top finishers were both Italian and representing Telefonica teams, there were 8 - 2 = 6 top finishers who represented Telefonica but were not Italian. Thus, statement (2) is also sufficient to answer the question.
Answer: D.
General Discussion
11 Jul 2016, 11:30
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Draw an overlapping set matrix! This is the perfect problem for it.
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